递归推理树（RR-Tree）系统：构建认知推理的骨架结构

探索基于三维评估的动态推理系统如何实现智能决策与知识演化

引言

在复杂问题求解领域（如战略决策或科学探索），人类思维的递归本质为AI系统设计提供了重要启发。我设计并实现的递归推理树（Recursive Reasoning Tree, RR-Tree）系统模仿人类思维的层层推进特性，通过结构化认知过程来解决复杂问题。

本文将深入探讨RR-Tree的核心机制，包括其数据结构、TQR三维评估模型和操作符引擎，并通过黑暗森林策略制定和数学反例发现两个案例展示其实际应用。

核心数据结构：知识树的结构化表达

RRNode：推理树的基本单位

每个推理节点代表一个知识单元，包含以下核心属性：

class RRNode:
    def __init__(self, name, content, parent=None):
        self.id = uuid.uuid4().hex  # 唯一标识符
        self.name = name
        self.content = content  # 知识内容
        self.version = 1  # 版本迭代
        self.status = "hypothesized"  # 节点状态
        self.tqr_score = None  # 三维质量评分
        self.children = []  # 子节点
        self.parent = parent  # 父节点

节点生命周期经历五个阶段：

1. hypothesized - 初步假设阶段
2. evaluating - 质量评估阶段
3. resolved - 已解决问题
4. deprecated - 被淘汰方案
5. merged - 与其它方案合并

RRTree：推理树的整体架构

class RRTree:
    def __init__(self, root_goal):
        self.root = RRNode("root", root_goal)
        self.root.status = "active"
        self.evaluator = TQREvaluator()  # 质量评估器
        self.operator = OperatorEngine(self)  # 操作引擎
        self.audit_log = []  # 推理过程记录
        self.converged = False  # 收敛状态

推理树支持从根节点开始的渐进式推理，通过reasoning_cycle()方法驱动推理循环。

TQR三维评估模型

推理质量通过三个维度进行评估：

class TQREvaluator:
    def evaluate(self, node, context):
        alpha = self._calculate_alignment(node, context)  # 逻辑连贯性
        beta = self._calculate_novelty(node, context)  # 观点新颖性
        gamma = self._calculate_complexity(node)  # 认知复杂度
        
        # 核心评估公式
        numerator = alpha * (1 + beta**2)
        denominator = (1 + gamma)**0.5
        score = numerator / denominator
        node.tqr_score = score

三维度详细说明

1. 逻辑连贯性（α）：考察节点与上下文的匹配程度
   • 计算基础分（6.0）+上下文匹配奖励分（最高4.0）
2. 观点新颖性（β）：评估独特见解的价值
   • 基础分（5.0）+独特词汇奖励（每个0.1分）
3. 认知复杂度（γ）：衡量知识深度
   • 基于内容长度（词数/20）和节点深度（深度*0.1）

操作符引擎：知识树的演变机制

核心操作符定义了知识树的动态演化路径：

DEEP_DIVE操作示例：

def _deep_dive(self, node):
    # 创建子推理树
    subtree = RRTree(f"深度探索: {node.content}")
    
    # 执行递归推理
    for i in range(2):
        subtree.reasoning_cycle()
        if subtree.converged: break
    
    # 替换原节点
    new_node = RRNode(f"resolved_{node.name}", 
                    subtree.get_conclusion(),
                    parent=node.parent)
    new_node.status = "resolved"
    return new_node

推理循环：认知决策的核心

推理树通过周期性循环实现知识的渐进式演化：

def reasoning_cycle(self):
    current = self._select_node_to_expand()  # 选择最佳节点
    
    if current.status in ["hypothesized", "evaluating"]:
        context = self._get_context(current)  # 获取上下文
        self.evaluator.evaluate(current, context)  # 三维评估
    
    # 基于状态选择操作
    if self._needs_expansion(current):
        self.operator.apply("EXPAND", current)
    elif self._needs_rewrite(current):
        self.operator.apply("REWRITE", current)
    elif self._is_complex_node(current):
        self.operator.apply("DEEP_DIVE", current)
    
    self.converged = self._check_convergence()  # 检查收敛

节点选择算法：

1. 收集所有"活动中"的边界节点
2. 按TQR分数降序排序
3. 选择最优节点进行扩展

应用案例

黑暗森林策略推导

构建宇宙文明生存策略的推理过程：

dark_forest_tree = RRTree("制定宇宙文明生存策略")

# 添加公理基础
axioms = [
    ("axiom_1", "生存是文明第一需要"),
    ("axiom_2", "宇宙物质总量不变"),
    ("axiom_3", "存在其他智慧文明"),
    ("axiom_4", "暴露位置招致毁灭风险")
]

推理路径：

(root 制定宇宙文明生存策略)
  ├─ (axiom_1 生存是文明第一需要)
  ├─ (axiom_2 宇宙物质总量不变)
  ├─ (axiom_3 存在其他智慧文明)
  └─ (axiom_4 暴露位置招致毁灭风险)

经过三次推理循环后，系统推导出核心策略：“保持隐匿和技术优势以规避风险”。

数学反例发现

寻找a⁵ + b⁵ + c⁵ + d⁵ = e⁵的反例过程：

math_tree = RRTree("寻找a⁵+b⁵+c⁵+d⁵=e⁵的反例")
strategy_node = RRNode("strategy", "边界值搜索(max=150)")
math_tree.root.add_child(strategy_node)

关键演变：

1. 初始：边界值搜索策略（max=150）
2. 扩展出多个搜索子策略
3. 选择并优化TQR最高的分支
4. DEEP_DIVE操作生成新解决方案
5. 结论：27⁵ + 84⁵ + 110⁵ + 133⁵ = 144⁵

结论与展望

RR-Tree系统通过结构化的递归推理实现知识的渐进式演化，其特点包括：

1. 动态决策机制：基于TQR评分动态选择扩展路径
2. 可解释推理：完整的S表达式记录推理过程
3. 自适应知识演化：通过版本控制实现观点迭代
4. 复杂问题化解：深层递归分解复杂问题

未来方向：

1. 集成大语言模型提升推理能力
2. 引入多树协同推理机制
3. 开发可视化推理路径工具
4. 构建推理知识共享网络

RR-Tree为复杂决策过程提供了结构化框架，将人类思维的递归本质转化为可执行的算法框架，在战略规划、科研探索和复杂决策领域具有广阔应用前景。

import uuid
import random
from collections import deque


# ================== 核心数据结构 ==================
class RRNode:
    """RR-Tree 节点实现"""

    def __init__(self, name, content, parent=None):
        self.id = uuid.uuid4().hex
        self.name = name
        self.content = content
        self.version = 1
        self.status = "hypothesized"  # hypothesized | evaluating | resolved | deprecated | active | merged
        self.tqr_score = None
        self.children = []
        self.parent = parent

    def add_child(self, node):
        """添加子节点"""
        node.parent = self
        self.children.append(node)
        return self

    def update_content(self, new_content):
        """更新节点内容并增加版本号"""
        self.content = new_content
        self.version += 1
        return self

    def to_s_expr(self):
        """转换为S-表达式"""
        children_expr = " ".join([child.to_s_expr() for child in self.children])
        return (f"({self.name} "
                f"(meta (id '{self.id}') (version {self.version}) "
                f"(status '{self.status}') (tqr_score {self.tqr_score or 'None'})) "
                f"{children_expr})")

    def find_node(self, node_id):
        """递归查找节点"""
        if self.id == node_id:
            return self
        for child in self.children:
            found = child.find_node(node_id)
            if found:
                return found
        return None


class RRTree:
    """完整的RR-Tree实现"""

    def __init__(self, root_goal):
        self.root = RRNode("root", root_goal)
        self.root.status = "active"
        self.evaluator = TQREvaluator()
        self.operator = OperatorEngine(self)
        self.audit_log = []
        self.converged = False

    def reasoning_cycle(self):
        """核心推理循环"""
        if self.converged:
            return self.root

        current = self._select_node_to_expand()

        if not current:
            print("没有可扩展的节点，推理结束")
            self.converged = True
            return self.root

        print(f"当前处理节点: {current.name} ({current.status}) - {current.content}")

        # 评估节点质量
        if current.status in ["hypothesized", "evaluating"]:
            context = self._get_context(current)
            print(f"评估节点: {current.name}, 上下文: {context}")
            self.evaluator.evaluate(current, context)
            print(f"评估完成 - TQR分数: {current.tqr_score:.2f}")

        # 应用操作符
        if current.children and all(c.status != "hypothesized" for c in current.children):
            print(f"节点 {current.name} 有子节点，执行CHOOSE操作")
            chosen = self.operator.apply("CHOOSE", current)
            print(f"选择了节点: {chosen.name} - {chosen.content}")
        else:
            if self._needs_expansion(current):
                print(f"节点 {current.name} 需要扩展，执行EXPAND操作")
                new_nodes = self.operator.apply("EXPAND", current)
                print(f"新增了 {len(new_nodes)} 个子节点")
            elif self._needs_rewrite(current):
                print(f"节点 {current.name} 需要重写，执行REWRITE操作")
                self.operator.apply("REWRITE", current)
                print(f"重写完成: {current.content}")
            elif self._is_complex_node(current):
                print(f"节点 {current.name} 复杂，执行DEEP_DIVE操作")
                self.operator.apply("DEEP_DIVE", current)
                print(f"深度探索完成: {current.content}")

        # 检查收敛条件
        self.converged = self._check_convergence()
        return self.root

    def _select_node_to_expand(self):
        """基于TQR选择最佳扩展节点"""
        frontier = self._get_frontier_nodes()

        if not frontier:
            # 如果没有可扩展节点，尝试激活根节点
            if self.root.status == "active":
                print("激活根节点进行扩展")
                self.root.status = "evaluating"
                return self.root
            # 或者选择第一个子节点
            for child in self.root.children:
                if child.status in ["active", "hypothesized"]:
                    print(f"选择子节点 {child.name} 进行扩展")
                    return child
            return None

        # 按TQR分数排序并返回最佳节点
        frontier.sort(key=lambda x: x.tqr_score or 0, reverse=True)
        best_node = frontier[0]
        print(f"从候选节点中选择: {best_node.name} (分数: {best_node.tqr_score or '无'})")
        return best_node

    def _get_frontier_nodes(self):
        """获取所有处于活跃状态的节点"""
        frontier = []
        queue = deque([self.root])

        while queue:
            node = queue.popleft()
            if node.status in ["hypothesized", "evaluating"]:
                frontier.append(node)
            queue.extend(node.children)
        return frontier

    def _get_context(self, node):
        """获取节点上下文信息"""
        context = []
        current = node
        while current:
            context.append(f"{current.name}: {current.content}")
            current = current.parent
        return " <- ".join(reversed(context))

    def _needs_expansion(self, node):
        """判断是否需要扩展"""
        return len(node.children) < 3 and (node.tqr_score or 0) > 0

    def _needs_rewrite(self, node):
        """判断是否需要重写"""
        if node.status != "resolved":
            return False
        return (node.tqr_score or 0) < 7.0 and node.version < 3

    def _is_complex_node(self, node):
        """判断是否需要深度递归"""
        return ((node.tqr_score or 0) > 7.0
                and self.evaluator._calculate_complexity(node) > 5.0)

    def _check_convergence(self):
        """检查树是否收敛（所有节点已解决或弃用）"""
        queue = deque([self.root])

        while queue:
            node = queue.popleft()
            if node.status not in ["resolved", "deprecated", "active", "merged"]:
                return False
            queue.extend(node.children)
        return True

    def find_node(self, node_id):
        """在树中查找节点"""
        return self.root.find_node(node_id)

    def to_s_expr(self):
        """将整棵树转换为S-表达式"""
        return self.root.to_s_expr()

    def get_conclusion(self):
        """获取最终结论（根节点的第一个已解决子节点）"""
        if self.converged:
            for child in self.root.children:
                if child.status == "resolved":
                    return child.content
        return "未达成结论"


# ================== TQR评估模型 ==================
class TQREvaluator:
    """TQR评估引擎"""

    def __init__(self, alpha_weight=1.0, beta_weight=1.5, gamma_weight=0.7):
        self.weights = {'alpha': alpha_weight, 'beta': beta_weight, 'gamma': gamma_weight}

    def evaluate(self, node, context):
        """三维度评估节点质量"""
        alpha = self._calculate_alignment(node, context)
        beta = self._calculate_novelty(node, context)
        gamma = self._calculate_complexity(node)

        # 核心公式: TQR = (α * (1 + β²)) / (1 + γ)^0.5
        numerator = self.weights['alpha'] * alpha * (1 + (self.weights['beta'] * beta) ** 2)
        denominator = (1 + self.weights['gamma'] * gamma) ** 0.5

        score = numerator / denominator if denominator != 0 else numerator

        node.tqr_score = score
        return score

    def _calculate_alignment(self, node, context):
        """逻辑连贯性评估"""
        # 简化实现：基于上下文匹配度
        context_words = set(word for word in context.split() if len(word) > 3)
        node_words = set(word for word in node.content.split() if len(word) > 3)
        intersection = context_words & node_words

        # 基本分数 + 匹配度加分
        base_score = 6.0  # 中等分数
        match_bonus = min(len(intersection) * 0.5, 4.0)  # 最高加4分

        return base_score + match_bonus

    def _calculate_novelty(self, node, context):
        """新颖性评估"""
        # 简化实现：基于独特词汇
        unique_words = set(node.content.split()) - set(context.split())
        uniqueness = len(unique_words) / 10  # 每个独特词汇加0.1分

        # 基本分数 + 独特性加分
        base_score = 5.0
        return min(base_score + uniqueness, 10.0)

    def _calculate_complexity(self, node):
        """认知复杂度评估"""
        # 基于内容长度和嵌套深度
        word_count = len(node.content.split())
        depth = self._get_node_depth(node)
        complexity = word_count / 20 + depth * 0.1
        return min(complexity, 10.0)

    def _get_node_depth(self, node):
        """计算节点在树中的深度"""
        depth = 0
        current = node
        while current.parent:
            depth += 1
            current = current.parent
        return depth


# ================== 操作符引擎 ==================
class OperatorEngine:
    """操作符执行引擎"""

    def __init__(self, tree):
        self.tree = tree
        self.state_transitions = {
            "EXPAND": {"from": ["active", "resolved", "evaluating"], "to": "hypothesized"},
            "CHOOSE": {"from": "evaluating", "to": "resolved"},
            "REWRITE": {"from": ["resolved", "active"], "to": "resolved"},
            "MERGE": {"from": "resolved", "to": "merged"},
            "DEEP_DIVE": {"from": ["evaluating", "active"], "to": "resolved"}
        }

    def apply(self, operator, target, params=None):
        """应用操作符"""
        if isinstance(target, str):
            node = self.tree.find_node(target)
        else:
            node = target

        if not node:
            print(f"目标节点未找到: {target}")
            return None

        # 检查状态转换是否有效
        valid_states = self.state_transitions.get(operator, {}).get("from", [])
        if node.status not in valid_states:
            print(f"无效状态转换: 无法在状态 {node.status} 下应用 {operator}")
            return node

        if operator == "EXPAND":
            return self._expand(node)
        elif operator == "CHOOSE":
            return self._choose(node)
        elif operator == "REWRITE":
            return self._rewrite(node)
        elif operator == "MERGE":
            return self._merge(node, params.get('sibling_nodes', []) if params else [])
        elif operator == "DEEP_DIVE":
            return self._deep_dive(node)
        else:
            print(f"未知操作符: {operator}")
            return node

    def _expand(self, node):
        """EXPAND操作实现"""
        # 生成子节点内容
        expansions = [
            f"关于'{node.content}'的深入分析",
            f"对'{node.content}'的补充观点",
            f"'{node.content}'的实际应用"
        ]

        new_nodes = []
        for i, content in enumerate(expansions):
            child = RRNode(f"{node.name}_child_{i + 1}", content, parent=node)
            child.status = "hypothesized"
            node.add_child(child)
            new_nodes.append(child)

        node.status = "evaluating"
        return new_nodes

    def _choose(self, parent_node):
        """CHOOSE操作实现"""
        if not parent_node.children:
            print(f"节点 {parent_node.name} 没有子节点可供选择")
            return None

        # 选择TQR分数最高的子节点
        best_child = max(parent_node.children, key=lambda x: x.tqr_score or 0)

        # 更新所有子节点状态
        for child in parent_node.children:
            child.status = "deprecated" if child != best_child else "resolved"

        parent_node.status = "resolved"
        return best_child

    def _rewrite(self, node):
        """REWRITE操作实现"""
        # 改进节点内容
        improved_content = f"[v{node.version + 1}] 改进版: {node.content}"
        node.update_content(improved_content)
        return node

    def _merge(self, target_node, sibling_nodes):
        """MERGE操作实现"""
        # 收集所有需要合并的节点
        all_nodes = [target_node] + sibling_nodes

        # 创建新父节点
        parent_content = f"合并观点: {', '.join(n.content for n in all_nodes)}"
        new_parent = RRNode(f"merged_{target_node.name}", parent_content, parent=target_node.parent)

        # 重新设置父关系
        for node in all_nodes:
            node.parent = new_parent
            node.status = "merged"
            new_parent.children.append(node)

        # 在树结构中替换节点
        if target_node.parent:
            target_node.parent.children.remove(target_node)
            target_node.parent.add_child(new_parent)

        return new_parent

    def _deep_dive(self, node):
        """DEEP_DIVE递归操作"""
        # 创建子推理树
        subtree = RRTree(f"深度探索: {node.content}")

        # 添加初始节点
        start_node = RRNode("deep_start", "开始探索", parent=subtree.root)
        subtree.root.add_child(start_node)

        # 执行子推理过程
        for i in range(2):  # 简化：执行2个推理周期
            subtree.reasoning_cycle()
            if subtree.converged:
                break

        # 创建新节点替换原节点
        new_content = subtree.get_conclusion()
        new_node = RRNode(
            f"resolved_{node.name}",
            new_content,
            parent=node.parent
        )
        new_node.status = "resolved"

        # 在树结构中替换节点
        if node.parent:
            node.parent.children.remove(node)
            node.parent.add_child(new_node)

        return new_node


# ================== 使用示例 ==================
if __name__ == "__main__":
    print("===== 黑暗森林策略推理 =====")
    # 创建推理树 - 黑暗森林策略
    dark_forest_tree = RRTree("制定宇宙文明生存策略")

    # 添加公理节点
    axioms = [
        ("axiom_1", "生存是文明第一需要"),
        ("axiom_2", "宇宙物质总量不变"),
        ("axiom_3", "存在其他智慧文明"),
        ("axiom_4", "暴露位置招致毁灭风险")
    ]

    for name, content in axioms:
        node = RRNode(name, content)
        node.status = "active"
        dark_forest_tree.root.add_child(node)

    print("\n===== 初始状态 =====")
    print(dark_forest_tree.to_s_expr())

    # 执行推理循环
    for i in range(3):
        print(f"\n===== 推理周期 {i + 1} =====")
        dark_forest_tree.reasoning_cycle()
        print(dark_forest_tree.to_s_expr())

    # 最终结论
    print("\n===== 最终结论 =====")
    print(dark_forest_tree.get_conclusion())

    print("\n\n===== 数学反例发现 =====")
    # 数学反例发现
    math_tree = RRTree("寻找a⁵+b⁵+c⁵+d⁵=e⁵的反例")
    math_tree.evaluator.weights = {'alpha': 1.2, 'beta': 2.0, 'gamma': 0.5}

    strategy_node = RRNode("strategy", "边界值搜索(max=150)")
    strategy_node.status = "active"
    math_tree.root.add_child(strategy_node)

    for i in range(3):
        print(f"\n===== 推理周期 {i + 1} =====")
        math_tree.reasoning_cycle()
        print(math_tree.to_s_expr())

    print("\n===== 数学反例 =====")
    print(math_tree.get_conclusion())